Under uniform ergodicity and Lipschitz assumptions, the rescaled parameter process of multi-agent RL learners in a finite-state Markov game converges weakly to the ODE that averages each update against the stationary distribution of the fast game state.
Fluid Limits of Pure Jump Markov Processes: a Practical Guide
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abstract
A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much simpler than those in the outside literature. The result may be used to build parsimonious models of large random or pseudo-random systems.
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Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games
Under uniform ergodicity and Lipschitz assumptions, the rescaled parameter process of multi-agent RL learners in a finite-state Markov game converges weakly to the ODE that averages each update against the stationary distribution of the fast game state.